Numerical determination of long-range stress history from strain history in concrete

The paper presents an efficient and highly accurate step-by-step numerical algorithm for computation of stress history from any prescribed strain history in a linear age-dependent viscoelastic material. The method is applicable for any form of the creep function, including the typical case when the slope of the creep curve in the logarithmic time scale is significant over many orders of magnitude of the elapsed time period (i.e retardation spectrum is broad). The time division must be in geometric progression or nearly so. The creep function may be defined by formulas or by a table of values. A FORTRAN program is presented which allows quick and economical computer solution. Numerical examples are given and excellent convergence is demonstrated. For the special case of strains varying linearly with the creep coefficient a useful new theorem is proved.